Comparative analysis of unsteady magneto flow of tetra-hybrid nanofluid across stretchable cylinders under the impact of different nanoparticles shape

• Unsteady tetra hybrid nanofluids in a thermally radiative expandable or contractible cylinder is considered. • Heat transfer rate is discussed in terms of viscous dissipation, ohmic energy, and convective boundary conditions. • The influence of different nanoparticle shapes (spherical, cylindrical, platelet and blade) is systematically investigated. • Flow rate is improved against rising unsteadiness and electric parameters. • Nusselt number is enhanced for higher unsteadiness parameter, unlike skin friction, which is reduced. This study investigates the effects of uniform heat generation/absorption and Ohmic heating in an unsteady model of radiating flow of a tetra-hybrid nanofluid (thnf). This nanofluid is flowing over a linearly stretchable or shrinkable cylindrical surface. This unsteady model includes these parameters related to the properties of thermal radiation, magnetic and electric fields, viscous dissipation, and convective boundary conditions with four different nanoparticle shapes. Motivated by the wide-ranging applications of antifreeze agents in industrial, mechanical, nuclear and construction domains, an advanced model is developed considering water (H 2 O) based with these tetra-nanoparticles: titanium dioxide (TiO₂), Copper (Cu), aluminum oxide (Al 2 O 3 ), and silicon dioxide (SiO₂), wherein the influence of different nanoparticle shapes (spherical, cylindrical, platelet and blade) is also investigated. The analytical method, namely Homotopy Analysis Method (HAM), is implemented to solve the final equations in the form of ordinary differential equations (ODEs). This system of ODEs originates from the partial differential equations (PDEs) by employing similarity transformations. The results reveal that increasing the unsteadiness and electric field parameters enhances the fluid velocity, while porosity and magnetic field parameters exhibit a retarding influence. The Nusselt number near the surface increases with unsteadiness, whereas skin friction decreases. The study confirms that thnf substantially improves heat transfer and demonstrates promising potential for thermal regulation in cylindrical geometries, especially in cooling and antifreeze applications.